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An application of Siegel's formula over quaternion orders
Published online by Cambridge University Press: 26 February 2010
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Let Φ : L → ℤ be a positive definite even unimodular quadratic form, L ≅ ℤn; we put f(x) = Φ(x)/2 and call (L, f) a lattice, for short. Let min f be the minimum of the numbers f(x) ≠ 0. Fixing n (a multiple of 8), one is interested in the largest possible minimum. It follows from the theory of modular forms (cf. Sloane [6]) that
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